"Number of primes in intervals" "A million dollar problem"

Number of primes in intervals

Number of primes in an interval (0,m)

First (non-observational) formula – Recurrence relation

 The number of primes in the interval

- calculation according to the Sieve of Eratosthenes

(m) - Number integers (Total numbers)

 

Using the formula,      

 

we calculate the number of primes in the interval  

and further intervals 

  

Number of primes in an interval (0,х) – general formula

 

 

 

A million dollar problem

I decided to single out this problem as a separate topic and to simplify the variant in order to concentrate the attention of readers on the certain problem and not to expatiate through the whole issue. Although the problem is simple I take leave to say it shall not be solved in the nearest years. Someone of the readers may disprove my statement.

Find max. error of calculation of the number of primes in the interval

 

(Non-observational) formula to calculate the number of primes in the interval

 

Comments, if available, in Russian. 

Sergey Sitnikov